"Frankly, my dear, I don't give a damn" is a line from the 1939 film Gone with the Wind starring Clark Gable and Vivien Leigh. The line is spoken by Rhett Butler (Gable), as his last words to Scarlett O'Hara (Leigh), in response to her tearful question: "Where shall I go? What shall I do?"; Scarlett clings to the hope that she can win him back. This line is slightly different in Margaret Mitchell's 1936 novel Gone with the Wind, from which the film is derived: "My dear, I don't give a damn."

Source: Wikipedia